It’s fascinating how much of that carries over to subsequent metaphysical renditions.

Just goes to show....humans haven’t changed that much, from then to now.

Plato’s metaphysics is not systematic. It is problematic. It raises questions it cannot answer and problems that cannot be resolved. It is important to understand that this is a feature not a defect or failure. — Fooloso4

I think the first problem with that statement is that it ignores the fact that Plato's philosophy is primarily a way of life based on ethical values, the metaphysical justification for which (immortality of the soul, divine judgment in the afterlife, etc.) is clearly laid out in the dialogues.

Plato's metaphysical statements need not be "systematic" in the modern sense. The dialogues are not comprehensive philosophical treatises. A more detailed discussion of metaphysical questions could be carried out in the Academy for anyone interested.

There is nothing "problematic" about the Forms at all. They are comparable to universals. Particulars instantiate universals, but this doesn't mean that particulars and universals are one and the same thing.

There is no need for the Forms to be the Whole. It suffices for them to be steps leading to the Whole, or component elements by understanding which we understand the Whole.

And, of course, everything can be "problematic" if we want it to be. Take Marxist concepts like "the dictatorship of the proletariat" or "the withering away of the state" .... :smile:

I think the first problem with that statement is that it ignores the fact that Plato's philosophy is primarily a way of life based on ethical values, the metaphysical justification for which (immortality of the soul, divine judgment in the afterlife, etc.) is clearly laid out in the dialogues. — Apollodorus

I agree that it is a way of life. The question of the best life is of primary concern.

Where we disagree is that what you take to be a fact is not a fact but an interpretation. There are two different concerns here: how people ought to live and how I ought to live. The philosopher is not satisfied with what others say is the best way to live. She wants to figure that out for herself. Plato addresses both these concerns.

Metaphysics is not in the business of justification. It is free inquiry. It does not aim at a goal. But ethics involves persuasion. The story of the soul has proven to be very effective. But the philosopher asks whether it is true. Plato's metaphysics addresses the philosopher differently than he addresses others.

There is nothing "problematic" about the Forms at all. They are comparable to universals. Particulars instantiate universals, but this doesn't mean that particulars and universals are one and the same thing. — Apollodorus

The history of philosophy shows that 'universals' is not a problem free solution.

Metaphysics is not in the business of justification. It is free inquiry. It does not aim at a goal. But ethics involves persuasion. — Fooloso4

Metaphysics serves to form a theoretical framework through which the world is better understood and can be used to support ethics making it more persuasive. If you say that the Good is the first principle, this has a bearing on ethics.

Being a practical system, Ancient Greek philosophy focuses on living a righteous life. Metaphysical "problems" obviously come second.

Plus, if metaphysics "does not aim at a goal" and "is just free inquiry", then why worry about it not being systematic???

The history of philosophy shows that 'universals' is not a problem free solution — Fooloso4

There is no "problem free" philosophical system. In addition to the fact that Plato's system is more sketched than laid out in great detail, it is no worse than other 4th-century BC philosophies.

Ultimately, there is neither ‘this or that’ but ‘this and that’. The Whole is not reducible to One. The whole is indeterminate. — Fooloso4

I will take issue with the term "indeterminate" used here. As Socrates describes in The Philebus, The combination of the two parts of what you call a "dyad", such as the limited and the unlimited, produces a balance, an equality, which constitutes an existing thing, a particular. I don't think there is good reason to believe that this equality is "indeterminate". Further, Socrates insists that there must be a cause of these instances of balance, or equality, and it doesn't make sense to say that a caused thing is indeterminate. Once a thing has been caused, it has a determined existence as the thing which it is.

Metaphysics serves to form a theoretical framework through which the world is better understood and can be used to support ethics making it more persuasive. — Apollodorus

This is exactly what I am arguing cannot be done. There is no theoretical framework for a world that is indeterminate.

why worry about it not being systematic??? — Apollodorus

Not a worry. A statement of fact:

It is important to understand that this is a feature not a defect or failure. — Fooloso4

This is exactly what I am arguing cannot be done. There is no theoretical framework for a world that is indeterminate. — Fooloso4

If people believe in the Good as a higher principle and live their lives in harmony with what is good, then obviously it can be done. In fact, I think most people do something like that anyway.

Not a worry. A statement of fact — Fooloso4

If it is not a worry then there is no need to discuss it. And you can always create your own system that is more systematic if you so wish.

In the Philebus, Plato raises the problem of the “indeterminate dyad” . — Fooloso4

Where in the Philebus does Plato say "indeterminate dyad"? And where does he say that it is a "problem"?

This is exactly what I am arguing cannot be done. There is no theoretical framework for a world that is indeterminate. — Fooloso4

That the world is indeterminate is not a Platonic principle.

I will take issue with the term "indeterminate" — Metaphysician Undercover

The term indeterminate dyad is Aristotle's.

it doesn't make sense to say that a caused thing is indeterminate. — Metaphysician Undercover

Socrates insists that there must be a cause of these instances of balance, or equality, and it doesn't make sense to say that a caused thing is indeterminate. — Metaphysician Undercover

In the Timaeus two kinds of cause are identified:

https://thephilosophyforum.com/discussion/comment/601558

Once a thing has been caused, it has a determined existence as the thing which it is. — Metaphysician Undercover

It is not that it cannot be determined to exist. The intelligible world of Forms is fixed and determinate. What is unlimited cannot be determinate. It is without boundaries.

The term indeterminate dyad is Aristotle's. — Fooloso4

OK, if you want to switch to Aristotle's metaphysics, let's do that then. But why title the thread "Plato's Metaphysics"?

It is not that it cannot be determined to exist. The intelligible world of Forms is fixed and determinate. What is unlimited cannot be determinate. It is without boundaries. — Fooloso4

Aristotle demonstrated that "the unlimited", as prime matter, is physically impossible.

If people believe in the Good as a higher principle and live their lives in harmony with what is good, then obviously it can be done. In fact, I think most people do something like that anyway. — Apollodorus

Of course people can live lives that are regarded as good!

There is no theoretical framework for a world that is indeterminate. — Fooloso4

More precisely: shit happens.

If it is not a worry then there is no need to discuss it. — Apollodorus

There is a very good reason to discuss it. If there is no systematic account of the whole that is a very big idea. It points to the limits of human understanding. The limited cannot comprehend the unlimited. Know yourself!

The term indeterminate dyad is Aristotle's. — Fooloso4

I see. This reminds me of the other canard about Plato's supposed phrase "a noble lie" that of course is NOT Plato's phrase! :grin:

But it's good to see you admitting that "indefinite dyad" is Aristotle's term not Plato's.

And nor does Plato say that it is a "problem". It is YOU who says that!

OK, if you want to switch to Aristotle's metaphysics — Metaphysician Undercover

It is not Aristotle's metaphysics, it is Aristotle discussing Plato's metaphysics.

Of course people can live lives that are regarded as good! — Fooloso4

Exactly. They can and they do!

It points to the limits of human understanding. The limited cannot comprehend the unlimited. Know yourself! — Fooloso4

The limited may indeed be unable to comprehend the unlimited fully. But it may still comprehend some of it.

And of course, Plato says that the Good is knowable.

Perhaps you could provide a reference as to where Aristotle refers to Plato's metaphysics as being concerned with an "indeterminate" dyad. "Indeterminate dyad " appears oxymoronic to me, as a "dyad" consists of two defined terms, and therefore cannot be indeterminate. I haven't come across anywhere where Aristotle refers to Plato's metaphysics as concerning an indefinite dyad. Maybe you can point me in that direction.

Perhaps you could provide a reference as to where Aristotle refers to Plato's metaphysics as being concerned with an "indeterminate" dyad. — Metaphysician Undercover

One place is at 987b:

Accordingly the material principle is the "Great and Small," and the essence <or formal principle> is the One, since the numbers are derived from the "Great and Small" by participation in the the One.

.. it is peculiar to him to posit a duality instead of the single Unlimited, and to make the Unlimited consist of the "Great and Small."

Also:

For number is from one and the indeterminate dyad. (1081a through 1082a)

ἀόριστος δυάς (aoristos dyas) is indeed in Metaphysics:

Again, it must also be true that 4 is not composed of chance 2's. For according to them the indeterminate dyad, receiving the determinate dyad, made two dyads; for it was capable of duplicating that which it received (Meta. 1082a)

However, I think it is fair to say that, judging by past performance, “Fooloso4” is not only suggestive of “fool”, but it may be indicative of an agenda to “fool philosophers”. Therefore caution is advisable.

He has already admitted that "indeterminate dyad" is Aristotle, not Plato.

And he has still not produced any evidence of Plato's alleged phrase "a noble lie"! :smile:

One place is at 987b:

Accordingly the material principle is the "Great and Small," and the essence <or formal principle> is the One, since the numbers are derived from the "Great and Small" by participation in the the One.

.. it is peculiar to him to posit a duality instead of the single Unlimited, and to make the Unlimited consist of the "Great and Small." — Fooloso4

At this point Aristotle explains how Plato differs from the Pythagoreans. Plato assumed a duality (dyad), of sensible objects, and ideas, as two distinct types. The Pythagoreans, Aristotle says, believed that all sensible things were composed of numbers, ideas,

Also:

For number is from one and the indeterminate dyad. (1081a through 1082a) — Fooloso4

Here is an argument against the notion that a number is an object. If two is an object, it must be a distinct type of object from the two units which make up the two parts of the two. This makes two a different type of thing from one, and three would be a different type of thing from two, etc.. But in mathematical numbers, each number must be the same type of thing. This makes two, if it is an object, and the rest of the numbers if they are objects, something different from what mathematical numbers are supposed to be.

I think it is important to note that these are Aristotle's arguments against various proposals as to what kind of existence numbers have. There is no direct reference to Plato here, and the points listed by Aristotle, which he argues against, could very well be straw man points.

Again, it must also be true that 4 is not composed of chance 2's. For according to them the indeterminate dyad, receiving the determinate dyad, made two dyads; for it was capable of duplicating that which it received (Meta. 1082a)

There is a good point made here by Aristotle. If a two is composed of two units, a three composed of three units, and four composed of four units, then these are all determinate, mathematical numbers. But fi two is itself a unit, then when four is composed of two twos, these two units are not mathematical units, because the four is only made up of two. And we cannot say what value these units have, so they are indeterminate. Two of these units together (these units could be numbers of any value) could produce any number whatsoever, hence two as an object is termed an indeterminate dyad.

I think it is important to note that these are Aristotle's arguments against various proposals as to what kind of existence numbers have. There is no direct reference to Plato here, and the points listed by Aristotle, which he argues against, could very well be straw man points. — Metaphysician Undercover

I think it is obvious that in the Philebus Socrates (or Plato) simply introduces the principles of Unlimited or Infinite (apeiron) and Limited or Finite (peras) to explain how the construction of substances and qualities occurs according to the imposition of the Limited on the Unlimited.

This imposition cannot be random, it must happen by means of well-defined proportions, hence the third “Mixed” (meikte) principle that completes the "Triangle of Being" (or "Intelligible Triad"). This may be represented by a triangle with the angles Unlimited (A), Limited (B) and Mixed (C) where the latter is the apex. It is at this point that the Forms come into play. From this point, reality is organized by means of Forms which are manifestations of the Good.

A Form is the ideal Proportion, Ratio, or Measure whereby the two opposite principles, or “poles” of the continuum are combined to generate something that is beautiful, fitting, just, etc. The Good which is the principle of Goodness as well as the One is present in the Form which is at once unique and good, whilst also transcending it, in the same way the Form is at once present in and transcendent to, sensible particulars.

The Form of Triangularity, for example, is analyzable into the principle of Unlimited and the principle of Limited and their interaction which is Proportion or Measure. The Form is the ideal Ratio or Proportion that makes the ideal triangular shape that is instantiated to various degrees of perfection in all mathematical triangles and triangular objects.

In other words, it is Measure (metrike) that brings about numbers, geometrical magnitudes, speed, etc. that are discussed in the Republic as part of the mathematical education necessary as a preparation for dialectic, i.e. logic and philosophical inquiry proper.

Aristotle may discuss the “indeterminate dyad” for his own purposes but this is his problem not Plato's. Plato’s own position is perfectly logical and clear. There is nothing mysterious or “problematic” about it at all.

The problem is with number, but it is with number as understood by the Greeks, which is not the way we treat number.

Aristotle identifies three kinds of number:

arithmos eidetikos - idea numbers
arithmos aisthetetos - sensible number
metaxy - between
(Metaphysics 987b)

Odd as it may sound to us, the Greeks did not regard one as a number. One is the unit, that which enables us to count how many. How many is always how many ones or units or monads that are being counted. Countable objects require some one thing that is the unit of the count, whether it be apples, or pears, or pieces of fruit.

Eidetic numbers are not counted in the same way sensible numbers are. Eidetic numbers belong together in ways that units or monads do not.

The eidetic numbers form an ordered hierarchy from less to more comprehensive.

... the "first" eidetic number is the eidetic "two"; it represents the genos of being as such, which comprehends the two eide "rest and "change". (Jacob Klein, Greek Mathematical Thought and the Origins of Algebra).

In the Sophist the problem comes up of how to count the eidetic two.

Theaetetus:
We really do seem to have a vague vision of being as some third thing, when we say that motion and rest are.
Stranger:
Then being is not motion and rest in combination, but something else, different from them.
Theaetetus:
Apparently.
Stranger:
According to its own nature, then, being is neither at rest nor in motion.
Theaetetus:
You are about right.
Stranger:
What is there left, then, to which a man can still turn his mind who wishes to establish within himself any clear conception of being?
Theaetetus:
What indeed?
Stranger:
There is nothing left, I think, to which he can turn easily. (Sophist 250)

To count rest, change, and being as three would be mistaken. Being is a higher order than rest and change. It is not a third thing to be counted alongside them.

The Stranger identifies five Kinds. In addition to change, rest, and being, there is sameness and difference (Sophist 254c)

Sameness and difference is the most comprehensive indeterminate dyad.

Contrary to Parmenides, the Stranger says that it is not possible to give an account of being without introducing non-being. Non-being is understood as otherness or difference.

There can be no comprehensive account of being without a comprehensive account of non-being. But what is other is without limit and cannot be comprehended. On the one hand this means that there can never be a comprehensive account of the whole, but on the other, it encourages an openness to what might be; beyond our limits of comprehension.

On the one hand this means that there can never be a comprehensive account of the whole, but on the other, it encourages an openness to what might be; beyond our limits of comprehension. — Fooloso4

Plato’s statements should not be taken out of context. Of course there is an openness to things that are beyond our limits of comprehension. The whole point of Plato’s philosophy is to expand our understanding of the whole!

These so-called “problems” must be seen within the general system of principles in which the One or the Good is the ground of all knowledge.

This is why Plato urges the philosopher to strive to acquire direct knowledge of the One, not indulge in idle speculation about it.

A comprehensive account of the whole is impossible in ignorance of the One. Therefore the philosopher must rise to the perspective of the One where a grasp of the whole becomes possible. This is why Plato speaks of philosophy as “the upward way”, (ano odos), i.e. the way of vertical ascent (Rep. 621c).

See also:

[the study of geometry, etc.] would tend to draw the soul to truth, and would be productive of a philosophic attitude of mind, directing upward the faculties that now wrongly are turned earthward … (527b)

Everything is a matter of perspective. Without the right perspective and attitude of mind there can be no comprehension and everything seems forever “problematic” ….

The next phrase is:

“And must we not agree on a further point?” “What?” “That it is the knowledge of that which always is, and not of a something which at some time comes into being and passes away.” “That is readily admitted,” he said, “for geometry is the knowledge of the eternally existent.”

for geometry is the knowledge of the eternally existent — Wayfarer

Correct.

It is absolutely imperative to understand that, as stated in the Republic, the purpose of mathematics as applied by Plato is not to lose ourselves in endless speculative calculations but to constantly elevate and refine our thoughts toward the One.

If we are saying that one is a unit, then we must put two and two (or one and one) together.

The Indefinite Dyad may be described as a principle of complexity through which the One manifests multiplicity. However, like everything derived from the One, the Indefinite Dyad also has an element of unity. Thus the Dyad becomes the Number Two which represents at once (1) two units (2 x 1) that make up the number, and (2) the number itself that is a unity.

As Aristotle says, Plato teaches that from the Great and the Small, by participation in the One come the Forms and the Numbers:

Now since the Forms are the causes of everything else, he supposed that their elements are the elements of all things. Accordingly the material principle is the "Great and Small," and the essence <or formal principle> is the One, since the numbers are derived from the "Great and Small" by participation in the One (Meta. 978b)

In other words, the "Mixed" (Meikte), the third principle of the "Intelligible Triad" (Noete Trias) that combines the Great and the Small or the Unlimited and the Limited, is the function of the One whereby the One imposes limitation on itself in order to manifest multiplicity from Forms to Mathematical Objects to the multitude of Particulars that make up the sensible world.

The problem is with number, but it is with number as understood by the Greeks, which is not the way we treat number.

Aristotle identifies three kinds of number: — Fooloso4

We have a multitude of different kinds of numbers as well, natural numbers, rational numbers, real numbers, to name a few.

To count rest, change, and being as three would be mistaken. Being is a higher order than rest and change. It is not a third thing to be counted alongside them. — Fooloso4

I don't see your point

Therefore the philosopher must rise to the perspective of the One — Apollodorus

I suspect that is a no parking zone.

I am way outmatched here in terms of knowledge of Plato, so forgive my ignorance, I won't be providing quotes nor anything like that. I'll have to re-read some aspects of Plato sometime.

With that important note out of the way, there is something very alluring about Plato's forms. I am not speaking of mathematics here, which I know is extremely important, but more so of ideas. The ideal horse or tree or river and down the line with all the objects we categorize.

In a modern-ish context, it could be said that we are born with certain ideas latent in the mind, which grow as we grow up, both as a biological creature and as persons. The idea would be that if there exist other creatures capable of thought, they would have these objects "in them", only waiting to come to fruition as they develop.

Of course, there's the overwhelming possibility that minded creatures may have a nature that differs from ours and thus would not have exactly the same conceptions we have, but similar. This cannot be proved and resides outside of science - not in principle - but in our limits of understanding we bring to bear when we encounter the world as we are.

It's a beautiful train of thought - on the whole - and could even be useful to develop further with modern day knowledge being used.

I suspect that is a no parking zone. — Fooloso4

The temptation to Straussianize, Maimonidize, or Farabize Plato is understandable. But I think it must be resisted. I believe that Plato should be read on his own terms.

The One is Infinite or Unlimited. We may ask, Infinite or Unlimited what? Being, Life, Intelligence (Einai, Zoe, Nous). How can limited human intelligence grasp what has no limit?

Well, Plato tells us how. The only way of doing it is by letting go of whatever is limiting our intelligence, that is, concerns with limited and limiting things such as the body and other material objects and thoughts about them; by lifting our gaze upward; and by opening our heart, the eye of our soul, to the Light of the One, that it may flood, pervade, and take over our whole being and lift us from darkness to its infinite, ever-present, all-illumining, and life-bestowing radiance.

The mind as a whole must be turned away from the world of change until its eye can bear to look straight at reality, and at the brightest of all realities which is what we call the Good (Rep. 518c)

In other words, the Intelligence Plato is talking about, is no abstract concept! It is a live, living force, it is Life itself. Try saying “dead intelligence”. It doesn’t make sense! Intelligence IS Life and Life IS Intelligence. And because it is Life itself, not "my life", "your life", or “our life” but Life in its absolute, irresistible, brutal, and devastating totality that sweeps all individualism away, we cannot control or manipulate it, try to do so, or even think of trying.

Plato uses the dialogues to convey a unified metaphysical framework that is hierarchical and that leads from complexity to simplicity, culminating in the absolutely simple first principle of the One which is autoexplicable and unhypothetical, but also ineffable and unfathomable.

Being Goodness, the One also serves as the guiding principle in Plato’s ethics. So, the philosopher can start living an ethical life straight away, without waiting for a vision of the One that, at the end of the day, may or may not come.

However, Platonism is “the Upward Way”, the process of ascent to ever-higher levels of being and experiencing. Whilst we are living a righteous life, or as righteous as possible, Plato gives us something even higher to aspire to. He explains how the One creates multiplicity by first imposing limit on the unlimited, i.e., on itself, and then forming it into ideal building blocks that are harmoniously arranged to provide the ordered structure of the Cosmos.

This is all that can be said (for now) about the One because the One, as already stated, is beyond the grasp of the human mind. However, though beyond our grasp, the One is knowable to us. This is very important to understand and to always remember. Remembrance (anamnesis) in Platonism is absolutely essential. And there is One thing that must be remembered at all times, even when we are asleep.

The same applies to the Forms. Though normally beyond our grasp, they can be known. Indeed, the Forms are the very essence of cognition, they stand at the threshold of the Unmanifest to the Manifest, at the apex of the “Intelligible Triad”. And for Plato (as for Ancient Greeks in general) cognition is “seeing”. When we see something we see a “form” or “shape”. Hence “Form”, eidos, which means “that which is seen”, i.e., the form or shape of an object of sight, something that is “seen”, “grasped”, “understood”, or “known”.

To begin with, we can think about Forms. There is nothing wrong with that. And I am not talking about wild speculation or fantasizing. I am talking about cool, rational, methodical thinking along the lines suggested by the dialogues. Thinking about the Forms opens us up to the experience of them. The Forms lead us to the Good and knowledge of the Good leads to knowledge of the Forms.

Socrates says that the philosopher, i.e. the lover of wisdom or seeker after knowledge, can hit upon reality only by hunting down that reality alone by itself and unalloyed (Phaedo 66a).

The Forms are like the tracks of an animal we are hunting. Though we may have heard of it, we do not know the animal. All we see at first are clues that something has passed by through the forest: we notice changes in the behavior of other animals, we see broken twigs and leaves, trodden grass, etc. We may even hear some unfamiliar sounds in the distance, all pointing in the same direction.

Suddenly, we see prints left in the soil and something inexplicable happens within us. Our heart skips a beat, our hair stands on end, and deep down we know that we are on the right track. From that moment, we can no longer let go. As Socrates says, the philosophical quest “takes possession of our soul” (Phaedo 82d). We must follow the clues day and night. Eventually, though, after days, weeks, months or years, we see the animal itself and how it makes those prints. This enables us to fully understand the clues that led us to the quarry.

In his dialogues, Plato provides a description of the One, tells us what the tracks are that lead to the One, and gives us many other clues by means of myths, analogies, and logical arguments. I think we can hardly ask for more!

But the most important clue that Plato (or anyone else can give us) is the need of self-knowledge. Lack of self-knowledge means that we don’t know who or what we are. And this can only mean that we are not who or what we think we are! We must be something else.

As Plotinus says, to know ourselves we must know our Source: the human mind is a microcosm of the Cosmic Mind, the Supreme Intelligence and Ultimate Reality, and what we are hunting or looking for – or at least part of it – is already and always present within us. This is why we will never find it by looking for it in distant places, and even less by denying its existence.

We have a multitude of different kinds of numbers as well, natural numbers, rational numbers, real numbers, to name a few. — Metaphysician Undercover

What is at issue is not that there are different kinds of number, but what is different about the eidetic kind:

Eidetic numbers belong together in ways that units or monads do not. The eidetic numbers form an ordered hierarchy from less to more comprehensive. — Fooloso4

To count rest, change, and being as three would be mistaken. Being is a higher order than rest and change. It is not a third thing to be counted alongside them.
— Fooloso4

I don't see your point — Metaphysician Undercover

The point is that Being belongs to a higher intelligible order.

To count rest, change, and being as three would be mistaken. Being is a higher order than rest and change. It is not a third thing to be counted alongside them. — Fooloso4

In the Timaeus, the qualities of Being and Becoming are starkly differentiated:

For there were no days and nights and months and years before the heaven was created, but when he (the Demiurge) constructed the heaven, he constructed them also, they are all parts of time, and the past and future are created species of time, which we unconsciously but wrongly transfer to eternal being, for we say that it 'was,' or 'is' of 'will be,' but the truth is that 'is' alone is properly attributed to it, and that 'was' and 'will be' are only to be spoken of becoming in time, for they are motions, but that which is immovably the same forever cannot become older or younger by time. — Timaeus, 37e, translated by Benjamin Jowett

In the Theaetetus, the dyad of motion and rest is found to be insufficient to counter Protagoras' claim that 'man is the measure of all things.' Starting at 179c, an effort is begun to find an alternative to accepting the either/or of 'all things change' (as expressed by Heraclitus) against 'being never changes' (as put forth by Parmenides). As the dialogue proceeds, it is found that beings are encountered through the organs of perception but knowledge of those beings is different from perceiving them (186e). While that development puts Protagoras' claim to doubt, the problem of what knowledge is, in the realm of becoming, is not thereby resolved. The remainder of the dialogue tries out different explanations but finds none of them adequate to the challenge.

How does this sort of careful separation of different arguments relate to grand claims of explaining what is happening? It seems like Plato did both.